\[ y'(x)=-\frac {2 a}{128 a^4 x^3-96 a^3 x^2 y(x)^2-32 a^3 x^2+24 a^2 x y(x)^4+16 a^2 x y(x)^2-2 a y(x)^6-2 a y(x)^4-2 a-y(x)} \] ✓ Mathematica : cpu = 0.173741 (sec), leaf count = 126
\[\text {Solve}\left [8 a c_1=\frac {\text {RootSum}\left [-64 \text {$\#$1}^3 a^3+48 \text {$\#$1}^2 a^2 y(x)^2+16 \text {$\#$1}^2 a^2-12 \text {$\#$1} a y(x)^4-8 \text {$\#$1} a y(x)^2+y(x)^6+y(x)^4+1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\& \right ]}{a}+4 y(x),y(x)\right ]\]
✓ Maple : cpu = 0.079 (sec), leaf count = 41
\[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}+{\frac {\int ^{ \left ( y \left ( x \right ) \right ) ^{2}-4\,ax}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}}{8\,{a}^{2}}}-{\it \_C1}=0 \right \} \]